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Question 1 of 30
1. Question
There is a uniform electrostatic field in a region. The potential at various points on a small sphere, centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field?
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Question 2 of 30
2. Question
In a certain region static electric and magnetic fields exists. The magnetic field is given If a test charge moving with a velocity experiences no force in that region, then the electric field in the region, In SI units, is :
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Question 3 of 30
3. Question
A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by ∆T. The net change in its length is zero. Let l be the length of the rod, A its area of crosssection, Y its Young’s modulus, and α it coefficient of linear expansion. Then, F is equal to :
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Question 4 of 30
4. Question
A magnetic dipole in a constant magnetic field has :
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Question 5 of 30
5. Question
Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
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Question 6 of 30
6. Question
A small circular loop of wirer of radius is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = I_{o} cos (ωt). The emf induced in the smaller inner loop is nearly :
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Question 7 of 30
7. Question
Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
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Question 8 of 30
8. Question
In an experiment a sphere of aluminium of mass 0.20 kg is heated upto 150℃. Immediately, it is put into water of volume 150 cc at 27℃ kept in a claroimeter of water equivalent to 0.025 kg. Final temperature of the system is 40℃. The specific heat of aluminium is :
(take 4.2 Joule = 1 calorie)
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Question 9 of 30
9. Question
In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
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Question 10 of 30
10. Question
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s^{−1}. At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is
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Question 11 of 30
11. Question
An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (C_{p}) and at constant volume (C_{v}) is :
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Question 12 of 30
12. Question
The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 μC charge, its radius will be :
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Question 13 of 30
13. Question
An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t → ∞ is
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Question 14 of 30
14. Question
According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)
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Question 15 of 30
15. Question
Let the refractive index of a denser medium with respect to a rarer medium be n_{12} and its critical angle be θ_{C}. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by :
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Question 16 of 30
16. Question
A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ. If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)
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Question 17 of 30
17. Question
Two wires W_{1} and W_{2} have the same radius r and respective densities ρ_{1} and ρ_{2} such that ρ_{2} = 4ρ_{1}. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be an ode. The ratio of the number of antinodes formed in W_{1} to W_{2} is :
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Question 18 of 30
18. Question
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :
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Question 19 of 30
19. Question
Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?
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Question 20 of 30
20. Question
The VI characteristics of a diode is shown in the figure. The ratio of forward to reverse bias resistance is :
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Question 21 of 30
21. Question
The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :
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Question 22 of 30
22. Question
A potentiometer PQ is set up to compare two resistance as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K_{3} is open. The balance point is at a length l_{1} cm from P when two way key K_{3} is plugged in between 2 and 1, while the balance point is at a length l_{2} cm from P when key K_{3} is plugged in between 3 and 1. The ratio of two resistances is found to be :
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Question 23 of 30
23. Question
A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct statement.
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Question 24 of 30
24. Question
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is I_{o} as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :
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Question 25 of 30
25. Question
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh Radius of the Earth is 6400 km and g = 10 m/s^{2}.
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Question 26 of 30
26. Question
Magnetic field in a plane electromagnetic wave is given by
Expression for corresponding electric field will be :
Where c is speed of light.
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Question 27 of 30
27. Question
An engine operates by taking n moles of an ideal gas through the cycle ABCDA show in figure. The thermal efficiency of the engine is :
(Take C_{V} = 1.5 R, where R is gas constant)
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Question 28 of 30
28. Question
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :
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Question 29 of 30
29. Question
A 9 V battery with internal resistance of 0.5 Ω is connected across an infinite network as shown in the figure. All ammeters A_{1}, A_{2}, A_{3} and voltmeter V are ideal.
Choose correct statement.
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Question 30 of 30
30. Question
What is the conductivity of semiconductor sample having electron concentration of 5 × 10^{18} m^{−}^{3}, hole concentration of 5 × 10^{19} m^{−}^{3}, electron mobility of 2.0 m^{2} V^{−}^{1} s^{−}^{1} and hole mobility of 0.01 m^{2} V^{−}^{1} s^{−}^{1} ?
(Take charge of electron as 1.6 × 10^{−19} C)
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